A generalization of Banach's lemma and its applications to perturbations of bounded linear operators

Let X be a Banach space and let P:X→X be a bounded linear operator.Using an algebraic inequality on the spectrum of P,we give a new sufficient condition that guarantees the existence of(I-P)^(-1) as a bounded linear operator on X,and a bound on its spectral radius is also obtained.This generalizes the classic Banach lemma.We apply the result to the perturbation analysis of general bounded linear operators on X with commutative perturbations.

Some notes on the spectral perturbations of the signless Laplacian of a graph

Let G be a simple graph and let Q（G） be the signless Laplacian matrix of G. In this paper we obtain some results on the spectral perturbation of the matrix Q（G） under an edge addition or an edge contraction.

Best performance analysis for stochastic perturbation systems with spectral factorization

We investigate the best performance for linear feedback control systems in the case that plant uncertainty is to be considered. First, we define an average integral square criterion of tracking error over a class of stochastic model errors. By utilizing spectral factorization to minimize the performance index, we derive an optimal controller design method and further study best performance in the presence of stochastic perturbation. The results can be used to evaluate optimal performance in practical control system designs.

Characteristics of spectral-hole burning in Tm^(3+):YAG based on the perturbation theory

In this paper, the physical mechanism of the interaction between electromagnetic wave and spectral-hole burning crystal material is investigated in detail. In the small signal regime, a perturbation theory model is used to analyze the mechanism of spectral-hole burning. By solving the Liouville equation, three-order perturbation results are obtained. From the theoretic analysis, spectral-hole burning can be interpreted as a photon echo of the zero-order diffraction echo when the first optical pulse and the second optical pulse are overlapped in time. According to the model, the spectral-hole width is dependent on the chirp rate of the reading laser. When the chirp rate is slow with respect to the spectral features of interest, the spectral hole is closely mapped into time domain. For a fast chirp rate, distortions are observed. The results follow Maxwell-Bloch model and they are also in good agreement with the experimental results.

Study on Multi-Scale Blending Initial Condition Perturbations for a Regional Ensemble Prediction System

An initial conditions （ICs） perturbation method was developed with the aim to improve an operational regional ensemble prediction system （REPS）. Three issues were identified and investigated： （1） the impacts of perturbation scale on the ensemble spread and forecast skill of the REPS; （2） the scale characteristic of the IC perturbations of the REPS; and （3） whether the REPS＇s skill could be improved by adding large-scale information to the IC perturbations. Numerical experiments were conducted to reveal the impact of perturbation scale on the ensemble spread and forecast skill. The scales of IC perturbations from the REPS and an operational global ensemble prediction system （GEPS） were analyzed. A ＂multi-scale blending＂ （MSB） IC perturbation scheme was developed, and the main findings can be summarized as follows： The growth rates of the ensemble spread of the REPS are sensitive to the scale of the IC perturbations; the ensemble forecast skills can benefit from large-scale perturbations; the global ensemble IC perturbations exhibit more power at larger scales, while the regional ensemble IC perturbations contain more power at smaller scales; the MSB method can generate IC perturbations by combining the small-scale component from the REPS and the large-scale component from the GEPS; the energy norm growth of the MSB-generated perturbations can be appropriate at all forecast lead times; and the MSB-based REPS shows higher skill than the original system, as determined by ensemble forecast verification.

同质区共享端元变异性的高光谱混合像元分解

由于不同的照明条件、复杂的大气环境等因素,相同端元的光谱特征在图像的不同位置呈现出可见的差异,这种现象被称为端元的光谱变异性。在相当大的场景中,端元的变异性可能很大,但在适度的局部同质区内,变异性往往很小。扰动线性混合模型(Perturbed Linear Mixing Model,PLMM)在解混的过程中可以减轻端元变异性造成的不利影响,但是对缩放效应造成的变异性的处理能力较弱。为此,本文改进了扰动线性混合模型,引入了尺度因子以处理缩放效应造成的变异性,并结合超像素分割算法划分局部同质区,然后设计出基于局部同质区共享端元变异性的解混算法(Shared Endmember Variability in Unmixing,SEVU)。与扰动线性混合模型,扩展线性混合模型(Extended Linear Mixing Model,ELMM)等算法相比,所提SEVU算法在合成数据集上平均端元光谱角距离(mean Spectral Angle Distance,mSAD)和丰度均方根误差(abundance Root Mean Square Error,aRMSE)最优,分别为0.0855和0.0562;在Jasper Ridge和Cuprite真实数据集上mSAD是最优的,分别为0.0603和0.1003。在合成数据集和两个实测数据集上的实验结果验证了SEVU算法的有效性。

考虑时变特性的车-桥耦合系统非平稳振动频域方法研究

当列车行驶经过桥梁时,由于车辆在桥上的位置随时间不断变化,车-桥耦合系统具有时变特性,即使假设轨道不平顺为平稳激励,车辆和桥梁的振动仍然是一种非平稳的随机过程。本研究旨在提出一种非平稳频域分析方法,以高效分析受轨道不平顺激励的车-桥耦合系统的非平稳随机振动问题。首先推导了单节列车通过单跨简支桥的耦合系统时变频响传递函数(FRF),据此描述线性时变系统的动力特性。该函数满足一组变系数微分方程,可采用摄动法求解该函数,从而提高计算效率。随后,结合PRIESTLEY的演化谱理论,推导非平稳随机响应的演化功率谱密度函数(EPSD)。基于非平稳频域分析方法,计算响应时变均值和方差,结合3σ准则来估计非平稳响应的极值。研究结果表明,由于轨道不平顺的影响,车辆振动表现出平稳随机过程的特性,但其方差较大,表现出更大的离散性;而桥梁的振动则呈现出明显的非平稳特性,但方差较小,响应具有较小的随机性。极值分析表明,轨道不平顺激励对车辆振动具有显著影响,其均方根对极值响应起主导作用。而轨道不平顺激励对桥梁振动的影响较小,桥梁振动则主要受移动质量影响,其响应的极值主要受均值的影响。此外,相较于系统位移响应,车速对加速度响应的影响更为显著,例如车身加速度响应最大值随车速的增加可增大至3倍左右。

有界线性算子的谱半径与扰动

广义逆理论在数值线性代数、数值分析、最优化、控制论、数理统计、微分方程及应用数学中具有引人注目的应用,其中算子广义逆在求解线性算子方程的极值解、最小范数解与最佳逼近解时发挥重要作用.设X为Banach空间,T:X→X为具有闭值域的有界线性算子.利用谱半径代替范数作为刻画扰动算子的工具,在扰动算子是可交换的假设下,减弱了可逆算子方程的经典扰动结果和一般算子方程的最优扰动结果的前提条件.同时,也利用谱半径代替范数作为刻画扰动算子的工具,减弱了Banach空间有界线性算子T的广义逆的经典扰动结果的前提假设,获得了利用谱半径的更加精细的扰动误差估计.

二阶奇异摄动问题的新的谱元方法

由于二阶奇异摄动问题的解具有边界层,用传统的数值方法很难得到理想的逼近效果.为了高效地求解此类问题,对区间做剖分,分别使用移位的映射Legendre多项式和传统Legendre多项式作为基函数,提出新型混合谱元法.该方法能够更好地模拟解在边界层附近的奇异行为.数值结果验证了所提方法的高效性.

Spectral entropy analysis of different alpha band rhythms in relation to hand motor imagery

The event-related desynchronization/synchronization(ERD/ERS) time courses of lower and upper alpha band rhythms during hand motor imagery are investigated respectively by Fourier Sectral Entropy (FSE) in this paper. By analyzing one group of BCI competition data, it was found that FSE within upper alpha band displays a pronounced increase and decrease over contralateral and ipsilateral brain areas respectively at the onset of hand motor imagery, which is corresponding to the antagonistic ERD/ERS patterns in previous studies. Different from the upper alpha activity pattern, FSE within lower alpha band displays a consistent increase over both two hemispheres hand representative areas. The preliminary results show that FSE could disclose the different behaviors of the upper and lower alpha band rhythms so that a new idea with the complexity measure is provided to characterize functional dissociation of lower and upper frequency alpha rhythms in relation to hand motor imagery.

The Decomposability for Operator Matrices and Perturbations

Let X and Y be Banach spaces.For A∈L(X),B∈L(Y),C∈L(Y,X),let MCbe the operator matrix defined on X⊕Y by M_(C)=(AC0B)∈L(X⊕Y).In this paper we investigate the decomposability for MC.We consider Bishop’s property(β),decomposition property(δ)and Dunford’s property(C)and obtain the relationship of these properties between M_(C) and its entries.We explore how σ_(*)(M_(C))shrinks from σ_(*)(A)∪σ_(*)(B),where σ_(*)denotes σ_(β),σ_(δ),σ_(C),σ_(dec).In particular,we develop some sufficient conditions for equality σ_(*)(MC)=σ_(*)(A)∪σ_(*)(B).Besides,we consider the perturbation of these properties for MCand show that in perturbing with certain operators C the properties for MCkeeps with A,B.Some examples are given to illustrate our results.Furthermore,we study the decomposability for(0AB0).Finally,we give applications of decomposability for operator matrices.

Image registration based on matrix perturbation analysis using spectral graph

We present a novel perspective on characterizing the spectral correspondence between nodes of the weighted graph with application to image registration. It is based on matrix perturbation analysis on the spectral graph. The contribution may be divided into three parts. Firstly, the perturbation matrix is obtained by perturbing the matrix of graph model. Secondly, an orthogonal matrix is obtained based on an optimal parameter, which can better capture correspondence features. Thirdly, the optimal matching matrix is proposed by adjusting signs of orthogonal matrix for image registration. Experiments on both synthetic images and real-world images demonstrate the effectiveness and accuracy of the proposed method.

浅部异质体表面波探测方法研究

表面点源激发浅部波场由瑞利波主导且能量主要分布于一个波长深度,当瑞利波传播路径前方存在地下异质体时,瑞利波发生散射,在散射波的影响下振源与异质体之间的表面波场发生扰动,并且瑞利波穿过异质体能量衰减。基于这一现象,采用数值计算模拟均匀半空间异质体散射波场响应,分析不同异质体(空洞、软质体、硬质体)对表面波场的影响。研究表明,异质体区域谱密度与周围谱密度明显不同,根据谱扰动对应的偏移距预估异质体水平位置。而软质体、硬质体区域谱扰动特征较为特殊,软质体上方谱密度整体呈减弱趋势,硬质体上方谱密度整体呈增强趋势。可通过偏移距-波长谱图特征波长和谱密度预估埋深。

基于谱聚类的多数据流演化事件挖掘

为解决从多数据流挖掘演化事件这一难题,提出了一种多数据流上的谱聚类算法SCAM(spectral clustering algorithm of multi-streams),其相似矩阵基于耦合度构造,而耦合度衡量了两个数据流的动态相似性.提出了算法EEMA(evolutionary events mining algorithm),该算法基于聚类模型的演变挖掘多数据流的演化事件.定义了聚类模型凝聚度,用以衡量聚类的紧凑程度,并证明了凝聚度的上界.基于到上界的距离和规范化相似矩阵的特征间隙,定义了聚类模型质量,并作为EEMA的优化目标自动地确定聚簇数k.设计了O-EEMA作为EEMA的优化实现,其时间复杂度为O(cn2/2).在合成和真实数据集上的实验结果表明,EEMA和O-EEMA是有效的、可行的.

大尺度非饱和土壤水分运动的随机模型及有效参数的结构分析

本文将大尺度空间上的局部土壤水力特性及土壤水分变量视为三维统计平稳随机场的实现，在土壤参数及土壤水分变量的随机扰动均为小扰动的条件下，通过对描述小尺度非饱和土壤水分运动的数学模型进行平均处理，推导出描述大尺度非饱和土壤水分运动宏观特征的数学模型，模型的控制性方程与Ｒｉｃｈａｒｄｓ方程的形式是一样的．应用谱分析理论对层状土壤条件下模型有效参数及负压水头方差的结构进行了分析，通过分析得到有效参数是各向异性的，各向异性的程度与水分运动的状况有关，同时有效参数与负压水头方差还具有一定的滞后现象，且各向异性与滞后现象是由土壤特性的空间变异所引起的．

正定Hermite矩阵特征值的相对扰动界

给出了正定Hermite矩阵特征值的一个新扰动界,同以往的结论相比我们的界形式上更简洁而且新的扰动界在合同变换下保持不变。

高强度三次谐波转换对光束质量的影响

分别利用光强对比度和功率谱密度作为激光束的振幅调制和位相畸变的定量描述参量 ,研究了在高功率条件下 ,三次谐波转换过程对激光光束质量的影响 。

种群细胞中一类迁移算子的谱分析

在L^p(1≤p<+∞)空间上,研究了种群细胞中一类具扰动项的L-R模型的迁移方程,证明了这类模型相应的迁移算子产生的正C_0半群是紧的,从而得到了该迁移算子的谱仅由可数个具有限代数重数的离散本征值组成,且-∞是唯一可能的聚点等结果.

基于二极化校正的陆上气云区的转换波成像

柴达木盆地三湖地区地震资料受广泛发育的气云的影响,导致纵波在含气构造部位成像质量较差,而转换波勘探技术可望成为解决气云区成像问题的有效手段。本文以柴达木盆地涩北气田为实例,采用伪谱法对该区气云进行数值正演模拟;通过对模型数据的分析研究,可见到明显的二极化现象,该现象是影响转换波成像质量的重要因素;应用将转换波速度分解为基本速度和速度扰动的二极化校正方法,可消除转换波二极化效应的影响,提高转换波成像质量。采用上述方法对该区二维三分量地震数据进行处理,可在转换波数据上观测到明显的二极化现象,二极化校正方法的应用的确能提高气云区转换波成像质量。

采用光栅角色散的宽带二倍频及聚焦特性分析

针对带宽为20nm左右、中心波长为1053nm的线性啁啾宽带激光,分析了采用光栅角色散方式宽带二倍频的原理,讨论了光栅角色散性能及光栅加工误差引入的基频光位相扰动对二倍频光转换效率及聚焦特性的影响.研究结果表明:采用光栅角色散方式的宽带二倍频光的转换效率、脉冲宽度和带宽均明显增大;在0～22nm基频光带宽范围内,二倍频光均可保持80%左右的转换效率;对于入射基频光带宽为22nm的情况,光栅角色散率在30～80μrad/nm范围内变化时,宽带二倍频转换效率均可保持在70%以上;基频光有位相扰动时,二倍频光带宽对二倍频聚焦光斑的主瓣影响不大,但对旁瓣有一定的匀滑作用,采用光栅角色散方式宽带二倍频的聚焦光斑旁瓣的匀滑效果更为明显.